This study will evaluate the safety and effectiveness of combination therapy with peginterferon alfa-2b and ribavirin for treating hepatitis C virus (HCV) infection in HIV-infected patients. In studies of patients with hepatitis C alone, interferon alfa-2b plus ribavirin treatment eradicated the HCV in almost half the patients. Peginterferon alfa-2b is a compound that results from attaching a polyethylene glycol molecule to interferon alfa-2b. This compound stays in the blood longer than unmodified interferon alfa-2b, causing a higher blood concentration and thus maintaining activity against the hepatitis C virus.